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dispersers
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Plural form of disperser. |
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A disperser is a one-sided extractor. Where an extractor requires that every event gets the same probability under the uniform distribution and the extracted distribution, only the latter is required for a disperser. So for a disperser, an event * * * * A * ⊆ * { * 0 * , * 1 * * } * * m * * * * * {\displaystyle A\subseteq \{0,1\}^{m}} * we have: * * * * P * * r * * * U * * m * * * * * [ * A * ] * > * 1 * − * ϵ * * * {\displaystyle Pr_{U_{m}}[A]>1-\epsilon } * * Definition (Disperser): A * * * * ( * k * , * ϵ * ) * * * {\displaystyle (k,\epsilon )} * -disperser is a function * * * * D * i * s * : * { * 0 * , * 1 * * } * * n * * * × * { * 0 * , * 1 * * } * * d * * * → * { * 0 * , * 1 * * } * * m * * * * * {\displaystyle Dis:\{0,1\}^{n}\times \{0,1\}^{d}\rightarrow \{0,1\}^{m}} * * such that for every distribution * * * * X * * * {\displaystyle X} * on * * * * { * 0 * , * 1 * * } * * n * * * * * {\displaystyle \{0,1\}^{n}} * with * * * * * H * * ∞ * * * ( * X * ) * ≥ * k * * * {\displaystyle H_{\infty }(X)\geq k} * the support of the distribution * * * * D * i * s * ( * X * , * * U * * d * * * ) * * * {\displaystyle Dis(X,U_{d})} * is of size at least * * * * ( * 1 * − * ϵ * ) * * 2 * * m * * * * * {\displaystyle (1-\epsilon )2^{m}} * . |